You need a streaming server to broadcast live streams. You can use a free open source Icecast to broadcast MP3, AAC, OGG files over HTTP. You can also use free open source red5 to broadcast FLV (audio only), MP3, AAC files over RTMP protocol.

You can install a streaming server onto your own computer or a rented server (Some shared hostings plans also allow them to be installed). Alternatively you can use a service that provides streaming audio broadcasting for you.